Rayfield Lumina

This is absolutely amazing, it contains pretty much every single item I mentioned! Thanks you very much, I'll be sure to show this to the admin of my community. I'm starting to understand better how these features work, and I'm delighted to find out that, while some have a fee, some others are included in the Admin CP, ready to be implemented. Very exciting!
Now, this is something that exceeds my expectations, an entire shop filled with plugins and apps I didn't even know existed. I'm feeling somewhat overwhelmed right now by the possibilities, it's like discovering an entire new world! Sorry if I sound to naive, hehe, I'm too new to all this.
I'll be sure to have a look around the blog.
Excellent advice, I should have started by doing using thevsearch function. I must confess our own Search system seems to be a bit off, sometimes results you expect to come by do not, or particularly old content is unavaible. Reason for me not considering using it in the first place n.n''.
Mmm... sounds a little concerning, but understandable. I remember the admin mentioning once or twice that their priority was to keep the system running smoothly rather than implementing something that might cause trouble, so we'll have to see step by step what can be done. Trying out configurations on a "dummy" server sounds like the way to go. Thanks a lot for all the help!
Yes, I'm more than happy with the assistance provided so far, I'll report this to the admin in the hope that he finds these news attractive so he decides to implement some of the available features for the bettering of our community, so I'll take up on your offer and keep in contact as we discuss these ideas and any other doubts arise. Thank you!

This is absolutely amazing, it contains pretty much every single item I mentioned! Thanks you very much, I'll be sure to show this to the admin of my community. I'm starting to understand better how these features work, and I'm delighted to find out that, while some have a fee, some others are included in the Admin CP, ready to be implemented. Very exciting!
Now, this is something that exceeds my expectations, an entire shop filled with plugins and apps I didn't even know existed. I'm feeling somewhat overwhelmed right now by the possibilities, it's like discovering an entire new world! Sorry if I sound to naive, hehe, I'm too new to all this.
I'll be sure to have a look around the blog.
Excellent advice, I should have started by doing using thevsearch function. I must confess our own Search system seems to be a bit off, sometimes results you expect to come by do not, or particularly old content is unavaible. Reason for me not considering using it in the first place n.n''.
Mmm... sounds a little concerning, but understandable. I remember the admin mentioning once or twice that their priority was to keep the system running smoothly rather than implementing something that might cause trouble, so we'll have to see step by step what can be done. Trying out configurations on a "dummy" server sounds like the way to go. Thanks a lot for all the help!
Yes, I'm more than happy with the assistance provided so far, I'll report this to the admin in the hope that he finds these news attractive so he decides to implement some of the available features for the bettering of our community, so I'll take up on your offer and keep in contact as we discuss these ideas and any other doubts arise. Thank you!

You don’t need plugins for these. You can do both in your Admin CP.
- Reactions:
 
- Groups:
 

Plugins and Apps can be found here:
Downloads - Invision Community
Help Guides can be found here:
In addition to reading through the forums you can learn more about the platform by reading the company blogs:
Invision Community Blog - Invision Community
I would also recommend using the search function to see if any questions you may have in the future have already been answered by the IPS staff or other members. Sometimes you might find a thread that answers your question, and sometimes you won't, but it tends to be worth the effort overall.
This suite is highly configurable, but alas not every single option has a tutorial on how to set it up.  Many settings in one section of the ACP may impact other functionality so it's best not to make changes to the default settings without some thought as to the possible consequences.  I would recommend setting up a test server to try out things and when you are confident that a new feature works for your environment you implement it on your live server. 
Also note that some features like "Achievements" and reactions are setup for you on install. These features may or may not work for your community using the default settings so you may have to tweak them to work for you.
Often times admins think they know their community better than they actually do, as such, I would recommend working closely with your community to ensure the platform you develop works well for them.

As mentioned by others, some of these are available in the core software like member groups and changing the reaction images/names/points to what you want. Outside of that, there are third party applications/plugins in our Marketplace which you can easily install via the ACP which meet your needs to the other questions you had.
Please let us know if we can be of further assistance.